How Do You Derive the Kinematic Equation \(v_f^2 = v_i^2 + 2ad\)?

[Lego]

Homework Statement

Derive (v_f)^2 = (v_i)^2 +2ad

Homework Equations

(v_f)^2 = (v_i)^2 + 2ad
(v_f) = (v_i) + at
d = (v_i)t + \frac{1}{2}at^2

The Attempt at a Solution

I have attempted to replace the variables with others from other kinematic equations such as v_f = v_i + at. However, I am getting no where. I have also taken the derivative of the equation (or so I think) but if I have not done it correctly, then I am just going no where.

When taking the derivative of the equation (v_f^2 = v_i^2 + 2ad) I remembered dv/dt = a , a in this equation is constant, and dd/dt = v, thus I got 2a=2a+2v and once simplified brings me to 0=v? I feel I am deriving the equation incorrectly.

Now, after having exhausted my thoughts, I've come asking for help.

 

[learningphysics]

Are you supposed to derive the equation from first principles? What i mean is are you allowed to use:

$$d = (v_i)t + \frac{1}{2}at^2$$

 

[Lego]

Yes. I can use any type of equation. And any principles. I'm just at a loss as to how to get started. I should be fine with a little nudge in the right direction.

 

[learningphysics]

Yes. I can use any type of equation. And any principles. I'm just at a loss as to how to get started. I should be fine with a little nudge in the right direction.

You can solve for t, in the equation vf = v0 + at... then substitute t into the d equation posted, that will give you the result.

 

[Lego]

You can solve for t, in the equation vf = v0 + at... then substitute t into the d equation posted, that will give you the result.

Thank you. I've got it now. I had returned to using the other equations, but the word "derive" kept making my brain do derivatives. I guess that's what I get for being a math minor and taking as few physics classes as possible.

Thank you, again.

 

[learningphysics]

Thank you. I've got it now. I had returned to using the other equations, but the word "derive" kept making my brain do derivatives. I guess that's what I get for being a math minor and taking as few physics classes as possible.

Thank you, again.

no prob.